Now I had a lot of possibilities, but I couldn't rule anything completely out, or in. I went to the hint finder, and it revealed a 1 in row 7, column 4.

4 _ _ _ _ _ 9 1 _
_ 8 _ 4 _ _ 7 3 _
3 _ 6 7 _ _ _ _ 4

_ _ _ _ _ 7 6 _ _
_ 5 _ _ _ _ 3 2 _
_ _ 3 5 _ _ _ _ _

9 _ _ 1 _ 8 2 _ 3
8 3 2 _ _ 6 _ 7 _
_ 1 4 _ _ _ _ _ 8

My question is qhat logic was used to reveal the 1 there in row 7, column 4? I had concluded that the 1 had to be in either column 4 or column 5 of row 7, but I can't figure out how it knew to rule out column 5, or conclude that the 1 should go in column 4.

If one really wants to know the answers to "why?", it is possible to use
the Solution by Steps facility. This has a full explanation of every move
made in sequence and produces an audit trail (which can be copied to
a text editor using Ctrl-A and Ctrl-C in the usual way).

As yet these amazingly helpful annotations are not included in the hint
facility (or so I believe as I have never used the hint facility) BUT their
presence in the Step-solver should be adequate for those wishing to
extend their own prowess by observing how solutions develop.

When I get stuck, I use the step-solver in order to check that my solution
grid is correct. Usually, I find that I have overlooked something! However,
sometimes I find that the solver gets stuck at the same place as myself
and then I search these fora for clues as to advanced techniques.

Perhaps the hint facility should NOT have a reason as then it can prompt
the user into thinking more deeply about possible reasons! Only if this
process fails would recourse to the step-solver then be necessary!

As indicated in this site, there is no real point in solvers as solvers (other
than as an exercise for programmers!!). However, the solver by steps is
a great aid to understanding. It creates a text file indicating what has been
done at each step of the solution process.

On difficulty with it is that it can take ages to start solving as it takes one
step for each initial value (ie the puzzle has a given digit in a given cell
and the solver takes a step to change the solution for that cell from the
start value of 123456789 to the single digit given. Worse than that, it
sometimes applies logic before it has set the initial values.

However, it is excellent at identifying "stop" points as (like the Hints on
this site) it does not include all the "advanced" facilities that can be
spotted by humans but which are difficult to program. A "trial and error"
facility is included for use when a stop-point is found. I prefer to avoid
the sites that use trial and error but the Solver can be asked to prove a
UNIQUE solution. With that confirmation, the challenge is then to find
a technique to reach it WITHOUT trial and error!

Elsewhere on the site are comments about six identified techniques (of
which five are programmed and one is out as a challenge to any budding programmers).

This is an example of the generated notes. A challenge could be to
derive the original puzzle from them! Unfortunately the limited space
for posting on this site distorts the grid layouts included - but it should
be possible to get the idea.

Thanks for the info. Put the web site you suggested in my favorites. Would be great if "dailysudoku.com" hint had the explanation with it, but your suggested site helps me even if it is a little unwieldly. Hard to develop my skill if I can't understand how they got the next number so an explanation is really helpful. Appreciate your help. Thanks.